{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_35ca4d6b5ab84d04195541bc33c133f6535577435b2569bb9c113d5241892b92","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_35ca4d6b5ab84d04195541bc33c133f6535577435b2569bb9c113d5241892b92","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"db49b0d0d13a2ddc1c12a7156b60853601bd7c10f01566826e7af3da5650cb82","published":"Fri, 03 Jul 2026 00:00:00 -0400","receipt_hash":"db49b0d0d13a2ddc1c12a7156b60853601bd7c10f01566826e7af3da5650cb82","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"db49b0d0d13a2ddc1c12a7156b60853601bd7c10f01566826e7af3da5650cb82","observed_at":"2026-07-03T04:43:38.241623Z","parent_run_hash":"f0e30469786257a5e74170498cacb4c028623bf32d6d06d4dbadc488960545be","published":"Fri, 03 Jul 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2606.03003v2 Announce Type: replace-cross \nAbstract: A latent world model built from an equivariant encoder and predictor inherits a provable symmetry of its training loss: when the dynamics carries a group $G$ acting on latents by an orthogonal representation $\\rho(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting a restricted slice of orientations mathematically determines it on the entire orbit. The symmetry survives a real Muon/AdamW+EMA+VICReg run -- composed residual $\\sim 10^{-6}$ after training, under any optimiser (intrinsic Vector-Neuron/e3nn parametrisation) -- and one-step error is flat across the group (5-seed medians: equivariant $\\times 1.00$ vs a higher-capacity non-equivariant baseline $\\times 12.7$ in 2D, $\\times 17.2$ in 3D), while that baseline fits the slice but breaks out-of-distribution. The flatness is not a synthetic artefact: on real-robot DROID end-effector trajectories the equivariant model stays flat across th","title":"Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group","url":"https://arxiv.org/abs/2606.03003","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.03003v2 Announce Type: replace-cross \nAbstract: A latent world model built from an equivariant encoder and predictor inherits a provable symmetry of its training loss: when the dynamics carries a group $G$ acting on latents by an orthogonal representation $\\rho(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting a restricted slice of orientations mathematically determines it on the entire orbit. The symmetry survives a real Muon/AdamW+EMA+VICReg run -- composed residual $\\sim 10^{-6}$ after training, under any optimiser (intrinsic Vector-Neuron/e3nn parametrisation) -- and one-step error is flat across the group (5-seed medians: equivariant $\\times 1.00$ vs a higher-capacity non-equivariant baseline $\\times 12.7$ in 2D, $\\times 17.2$ in 3D), while that baseline fits the slice but breaks out-of-distribution. The flatness is not a synthetic artefact: on real-robot DROID end-effector trajectories the equivariant model stays flat across th","title":"Exact equivariance, kept through training, buys zero-shot generalisation across the symmetry group","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-03T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.03003"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:f711fd3c1dd02c5a9c6f58644e087b94e56854af85642a605eafb0f58f3d16cd6cfdbec6c3ce74cc0a1307d4373a0d48d950620af8f74691184ac44422c6d90a","signer":"crovia.substrate","subject":{"observed_at":"2026-07-03T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.03003"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"6ecbd343816b398e6a4a24e4c771ab5c66ad76d850a5b3394348b759ee2fc101","leaf_index":275664,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"addebcfffc0582affb3c66b4dec82082eed6cd8788f157b14959f2cdfeae87c6","side":"right"},{"sibling":"3e3e664916f2c490ed0cc692084bcf59fafad508348e2d909bebb9e17e649a85","side":"right"},{"sibling":"fb7bfad4d698ca3a27d756449ad2a4d7d03a2e5ba8024f0a1447d032ff7201f5","side":"right"},{"sibling":"ec2154c3580e5c23533328c96913b6a914ffd186e24d48404492979052cb8614","side":"right"},{"sibling":"40b3783ff1e71d3ebb17984aaa4e13e65bd1e0f6fd9ad4e7b7dfdc4848e2a397","side":"left"},{"sibling":"d3634fa5229dabfd18f6b2c431c82a9824e42092f16e4d5ca24f7ff63b3f123e","side":"right"},{"sibling":"01f6ff086bf4ba57ce8ef2e69a75991694c44d99ba581de7d218b24d698e7b27","side":"left"},{"sibling":"afd7390845185d24208014fda1eda02563e823c07b9f4ce03d1011344ff5e6f8","side":"left"},{"sibling":"da9343635b180d3ddf07636b2a7814fcbf809adc1979958fa092ef6d16ef0db5","side":"right"},{"sibling":"1685b068d9bba0447845c97429c2a9ba728526abe2dc9d9522fed7b13d6620e4","side":"right"},{"sibling":"cf1e47b22a12b71fda307cbe1b98bc247fa4226ac8691ca8d99e6cc72a905b34","side":"left"},{"sibling":"4dbd8247ba08a5432c7d6540711da9acb2f59e6189865aa8552dee37f69286a9","side":"right"},{"sibling":"41cd1885dc3fcb51e49eeb887d6d22ec2cfa58df0e4f8d7c7dddf3a1b0ce8249","side":"left"},{"sibling":"8a09562f6b247c1c3cd1fea36cb3b8f1cf5c575479dd514573856a380a964bf5","side":"left"},{"sibling":"723981908169653ca6d835aa9b8381a8c7ad3e3e3830d0792bc32032cda615ee","side":"right"},{"sibling":"c0594fa1ee81d5f019cccc7b5e51af603c6d7e43995498c451012060c7d06165","side":"right"},{"sibling":"4de6a2fb22efbb50c84dc62abeb0f2cbc8c663a9540aeba9e758ebfdfe3e86dd","side":"right"},{"sibling":"fdbb3519f8dc411a4043dfb5abdbfea5441e130326183ac2247c42584033f152","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":275799,"merkle_root":"2581d0d6e5fa345cdf2e8ab3b191ace76d6b14189901ab0e4c2291ca1d1ae1e6","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260703T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-03T05:38:09Z","sig_algorithm":"ed25519","signature":"e44a386a5ae00c0e7fc67b1179bb9060bf0fefc006e454fec70e27668182ff497d1e2faf0c3b22de0917beefb7c80e880dae925a3f67e1b16aa0eb44bf947407","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_35ca4d6b5ab84d04195541bc33c133f6535577435b2569bb9c113d5241892b92"}}